Lesson 6

Welcome

Notes:

价格会随着克拉大小的增加而增加。 ***

Scatterplot Review

library(ggplot2)
ggplot(aes(x=carat,y=price),data = diamonds) + 
  xlim(0,quantile(diamonds$carat,0.99)) +
  ylim(0,quantile(diamonds$price,0.99)) +
  geom_point(fill = I('#F79420'),color=I('black'),shape=21)
## Warning: Removed 926 rows containing missing values (geom_point).


Price and Carat Relationship

Response:


Frances Gerety

Notes:

A diamonds is


The Rise of Diamonds

Notes:


ggpairs Function

Notes:

#install these if necessary
#install.packages('GGally')
#install.packages('scales')
#install.packages('memisc')
#install.packages('lattice')
#install.packages('MASS')
#install.packages('car')
#install.packages('reshape')
#install.packages('plyr')

# load the ggplot graphics package and the others
library(ggplot2)
library(GGally)
library(scales)
library(memisc)
## Loading required package: lattice
## Loading required package: MASS
## 
## Attaching package: 'memisc'
## The following object is masked from 'package:scales':
## 
##     percent
## The following objects are masked from 'package:stats':
## 
##     contr.sum, contr.treatment, contrasts
## The following object is masked from 'package:base':
## 
##     as.array
# sample 10,000 diamonds from the data set
set.seed(20022012)
diamond_samp <- diamonds[sample(1:length(diamonds$price), 10000), ]
ggpairs(diamond_samp, 
  lower = list(continuous = wrap("points", shape = I('.'))), 
  upper = list(combo = wrap("box", outlier.shape = I('.'))))
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

What are some things you notice in the ggpairs output? Response:


The Demand of Diamonds

Notes:

library(gridExtra)
plot1 <- qplot(x=price,data=diamonds,binwidth = 100,fill = I('#099DD9')) + 
  ggtitle('Price')

plot2 <- qplot(x=price,data=diamonds,binwidth = 0.01,fill = I('#F79420')) + 
  scale_x_log10() +
  ggtitle('Price (log10)')

grid.arrange(plot1,plot2,ncol = 2)


Connecting Demand and Price Distributions

Notes:


Scatterplot Transformation

qplot(carat,price,data=diamonds) +
  scale_y_continuous(trans = log10_trans()) +
  ggtitle('Price(log10)by carat')

Create a new function to transform the carat variable

cuberoot_trans = function() trans_new('cuberoot', transform = function(x) x^(1/3),
                                      inverse = function(x) x^3)

Use the cuberoot_trans function

ggplot(aes(carat, price), data = diamonds) + 
  geom_point() + 
  scale_x_continuous(trans = cuberoot_trans(), limits = c(0.2, 3),
                     breaks = c(0.2, 0.5, 1, 2, 3)) + 
  scale_y_continuous(trans = log10_trans(), limits = c(350, 15000),
                     breaks = c(350, 1000, 5000, 10000, 15000)) +
  ggtitle('Price (log10) by Cube-Root of Carat')
## Warning: Removed 1683 rows containing missing values (geom_point).


Overplotting Revisited

head(sort(table(diamonds$carat),decreasing = T))
## 
##  0.3 0.31 1.01  0.7 0.32    1 
## 2604 2249 2242 1981 1840 1558
head(sort(table(diamonds$price),decreasing = T))
## 
## 605 802 625 828 776 698 
## 132 127 126 125 124 121
ggplot(aes(carat, price), data = diamonds) + 
  geom_point(alpha = 0.5,size = 0.75,position = 'jitter') + 
  scale_x_continuous(trans = cuberoot_trans(), limits = c(0.2, 3),
                     breaks = c(0.2, 0.5, 1, 2, 3)) + 
  scale_y_continuous(trans = log10_trans(), limits = c(350, 15000),
                     breaks = c(350, 1000, 5000, 10000, 15000)) +
  ggtitle('Price (log10) by Cube-Root of Carat')
## Warning: Removed 1691 rows containing missing values (geom_point).


Other Qualitative Factors

Notes:


Price vs. Carat and Clarity

Alter the code below.

# install and load the RColorBrewer package
#install.packages('RColorBrewer')
library(RColorBrewer)
library(ggplot2)
ggplot(aes(x = carat, y = price,color = clarity), data = diamonds) + 
  geom_point(alpha = 0.5, size = 1, position = 'jitter') +
  scale_color_brewer(type = 'div',
    guide = guide_legend(title = 'Clarity', reverse = T,
    override.aes = list(alpha = 1, size = 2))) +  
  scale_x_continuous(trans = cuberoot_trans(), limits = c(0.2, 3),
    breaks = c(0.2, 0.5, 1, 2, 3)) + 
  scale_y_continuous(trans = log10_trans(), limits = c(350, 15000),
    breaks = c(350, 1000, 5000, 10000, 15000)) +
  ggtitle('Price (log10) by Cube-Root of Carat and Clarity')
## Warning: Removed 1693 rows containing missing values (geom_point).


Clarity and Price

Response:


Price vs. Carat and Cut

Alter the code below.

ggplot(aes(x = carat, y = price, color = cut), data = diamonds) + 
  geom_point(alpha = 0.5, size = 1, position = 'jitter') +
  scale_color_brewer(type = 'div',
                     guide = guide_legend(title = 'Cut', reverse = T,
                                          override.aes = list(alpha = 1, size = 2))) +  
  scale_x_continuous(trans = cuberoot_trans(), limits = c(0.2, 3),
                     breaks = c(0.2, 0.5, 1, 2, 3)) + 
  scale_y_continuous(trans = log10_trans(), limits = c(350, 15000),
                     breaks = c(350, 1000, 5000, 10000, 15000)) +
  ggtitle('Price (log10) by Cube-Root of Carat and Cut')
## Warning: Removed 1696 rows containing missing values (geom_point).


Cut and Price

Response:


Price vs. Carat and Color

Alter the code below.

ggplot(aes(x = carat, y = price, color = color), data = diamonds) + 
  geom_point(alpha = 0.5, size = 1, position = 'jitter') +
  scale_color_brewer(type = 'div',
                     guide = guide_legend(title = 'Color',
                                          override.aes = list(alpha = 1, size = 2))) +  
  scale_x_continuous(trans = cuberoot_trans(), limits = c(0.2, 3),
                     breaks = c(0.2, 0.5, 1, 2, 3)) + 
  scale_y_continuous(trans = log10_trans(), limits = c(350, 15000),
                     breaks = c(350, 1000, 5000, 10000, 15000)) +
  ggtitle('Price (log10) by Cube-Root of Carat and Color')
## Warning: Removed 1688 rows containing missing values (geom_point).


Color and Price

Response:


Linear Models in R

Notes:

Response:


Building the Linear Model

Notes: 为价格建立线性模型

m1 <- lm(I(log(price)) ~ I(carat^(1/3)), data = diamonds)
m2 <- update(m1, ~ . + carat)
m3 <- update(m2, ~ . + cut)
m4 <- update(m3, ~ . + color)
m5 <- update(m4, ~ . + clarity)
mtable(m1, m2, m3, m4, m5)
## 
## Calls:
## m1: lm(formula = I(log(price)) ~ I(carat^(1/3)), data = diamonds)
## m2: lm(formula = I(log(price)) ~ I(carat^(1/3)) + carat, data = diamonds)
## m3: lm(formula = I(log(price)) ~ I(carat^(1/3)) + carat + cut, data = diamonds)
## m4: lm(formula = I(log(price)) ~ I(carat^(1/3)) + carat + cut + color, 
##     data = diamonds)
## m5: lm(formula = I(log(price)) ~ I(carat^(1/3)) + carat + cut + color + 
##     clarity, data = diamonds)
## 
## ============================================================================================
##                        m1             m2             m3             m4            m5        
## --------------------------------------------------------------------------------------------
##   (Intercept)          2.821***       1.039***       0.874***      0.932***       0.415***  
##                       (0.006)        (0.019)        (0.019)       (0.017)        (0.010)    
##   I(carat^(1/3))       5.558***       8.568***       8.703***      8.438***       9.144***  
##                       (0.007)        (0.032)        (0.031)       (0.028)        (0.016)    
##   carat                              -1.137***      -1.163***     -0.992***      -1.093***  
##                                      (0.012)        (0.011)       (0.010)        (0.006)    
##   cut: .L                                            0.224***      0.224***       0.120***  
##                                                     (0.004)       (0.004)        (0.002)    
##   cut: .Q                                           -0.062***     -0.062***      -0.031***  
##                                                     (0.004)       (0.003)        (0.002)    
##   cut: .C                                            0.051***      0.052***       0.014***  
##                                                     (0.003)       (0.003)        (0.002)    
##   cut: ^4                                            0.018***      0.018***      -0.002     
##                                                     (0.003)       (0.002)        (0.001)    
##   color: .L                                                       -0.373***      -0.441***  
##                                                                   (0.003)        (0.002)    
##   color: .Q                                                       -0.129***      -0.093***  
##                                                                   (0.003)        (0.002)    
##   color: .C                                                        0.001         -0.013***  
##                                                                   (0.003)        (0.002)    
##   color: ^4                                                        0.029***       0.012***  
##                                                                   (0.003)        (0.002)    
##   color: ^5                                                       -0.016***      -0.003*    
##                                                                   (0.003)        (0.001)    
##   color: ^6                                                       -0.023***       0.001     
##                                                                   (0.002)        (0.001)    
##   clarity: .L                                                                     0.907***  
##                                                                                  (0.003)    
##   clarity: .Q                                                                    -0.240***  
##                                                                                  (0.003)    
##   clarity: .C                                                                     0.131***  
##                                                                                  (0.003)    
##   clarity: ^4                                                                    -0.063***  
##                                                                                  (0.002)    
##   clarity: ^5                                                                     0.026***  
##                                                                                  (0.002)    
##   clarity: ^6                                                                    -0.002     
##                                                                                  (0.002)    
##   clarity: ^7                                                                     0.032***  
##                                                                                  (0.001)    
## --------------------------------------------------------------------------------------------
##   R-squared            0.924          0.935          0.939         0.951          0.984     
##   adj. R-squared       0.924          0.935          0.939         0.951          0.984     
##   sigma                0.280          0.259          0.250         0.224          0.129     
##   F               652012.063     387489.366     138654.523     87959.467     173791.084     
##   p                    0.000          0.000          0.000         0.000          0.000     
##   Log-likelihood   -7962.499      -3631.319      -1837.416      4235.240      34091.272     
##   Deviance          4242.831       3613.360       3380.837      2699.212        892.214     
##   AIC              15930.999       7270.637       3690.832     -8442.481     -68140.544     
##   BIC              15957.685       7306.220       3761.997     -8317.942     -67953.736     
##   N                53940          53940          53940         53940          53940         
## ============================================================================================

Notice how adding cut to our model does not help explain much of the variance in the price of diamonds. This fits with out exploration earlier.

我们的数据是从2008年开始,所以不仅要考虑通货膨胀,而且钻石市场也绝对和今天不太一样。 实际上当用模型拟合此数据,并预测市场上钻石的价格时, ***

Model Problems

Video Notes:

Research: (Take some time to come up with 2-4 problems for the model) (You should 10-20 min on this)

Response:


A Bigger, Better Data Set

Notes:

#install.packages('bitops')
#install.packages('RCurl')
library('bitops')
library('RCurl')

load("BigDiamonds.rda")

The code used to obtain the data is available here: https://github.com/solomonm/diamonds-data

Building a Model Using the Big Diamonds Data Set

Notes:

diamondsbig$logprice <- log(diamondsbig$price)
m1 <- lm(logprice ~ I(carat^(1/3)),
         data = diamondsbig[diamondsbig$price < 10000 &
                              diamondsbig$cert == "GIA",])
m2 <- update(m1, ~. + carat)
m3 <- update(m2, ~. + cut)
m4 <- update(m3, ~. + color)
m5 <- update(m4, ~. + clarity)
mtable(m1,m2,m3,m4,m5)
## 
## Calls:
## m1: lm(formula = logprice ~ I(carat^(1/3)), data = diamondsbig[diamondsbig$price < 
##     10000 & diamondsbig$cert == "GIA", ])
## m2: lm(formula = logprice ~ I(carat^(1/3)) + carat, data = diamondsbig[diamondsbig$price < 
##     10000 & diamondsbig$cert == "GIA", ])
## m3: lm(formula = logprice ~ I(carat^(1/3)) + carat + cut, data = diamondsbig[diamondsbig$price < 
##     10000 & diamondsbig$cert == "GIA", ])
## m4: lm(formula = logprice ~ I(carat^(1/3)) + carat + cut + color, 
##     data = diamondsbig[diamondsbig$price < 10000 & diamondsbig$cert == 
##         "GIA", ])
## m5: lm(formula = logprice ~ I(carat^(1/3)) + carat + cut + color + 
##     clarity, data = diamondsbig[diamondsbig$price < 10000 & diamondsbig$cert == 
##     "GIA", ])
## 
## ================================================================================================
##                         m1              m2             m3             m4              m5        
## ------------------------------------------------------------------------------------------------
##   (Intercept)           2.671***        1.333***       0.949***       0.529***       -0.464***  
##                        (0.003)         (0.012)        (0.012)        (0.010)         (0.009)    
##   I(carat^(1/3))        5.839***        8.243***       8.633***       8.110***        8.320***  
##                        (0.004)         (0.022)        (0.021)        (0.017)         (0.012)    
##   carat                                -1.061***      -1.223***      -0.782***       -0.763***  
##                                        (0.009)        (0.009)        (0.007)         (0.005)    
##   cut: V.Good                                          0.120***       0.090***        0.071***  
##                                                       (0.002)        (0.001)         (0.001)    
##   cut: Ideal                                           0.211***       0.181***        0.131***  
##                                                       (0.002)        (0.001)         (0.001)    
##   color: K/L                                                          0.123***        0.117***  
##                                                                      (0.004)         (0.003)    
##   color: J/L                                                          0.312***        0.318***  
##                                                                      (0.003)         (0.002)    
##   color: I/L                                                          0.451***        0.469***  
##                                                                      (0.003)         (0.002)    
##   color: H/L                                                          0.569***        0.602***  
##                                                                      (0.003)         (0.002)    
##   color: G/L                                                          0.633***        0.665***  
##                                                                      (0.003)         (0.002)    
##   color: F/L                                                          0.687***        0.723***  
##                                                                      (0.003)         (0.002)    
##   color: E/L                                                          0.729***        0.756***  
##                                                                      (0.003)         (0.002)    
##   color: D/L                                                          0.812***        0.827***  
##                                                                      (0.003)         (0.002)    
##   clarity: I1                                                                         0.301***  
##                                                                                      (0.006)    
##   clarity: SI2                                                                        0.607***  
##                                                                                      (0.006)    
##   clarity: SI1                                                                        0.727***  
##                                                                                      (0.006)    
##   clarity: VS2                                                                        0.836***  
##                                                                                      (0.006)    
##   clarity: VS1                                                                        0.891***  
##                                                                                      (0.006)    
##   clarity: VVS2                                                                       0.935***  
##                                                                                      (0.006)    
##   clarity: VVS1                                                                       0.995***  
##                                                                                      (0.006)    
##   clarity: IF                                                                         1.052***  
##                                                                                      (0.006)    
## ------------------------------------------------------------------------------------------------
##   R-squared             0.888           0.892          0.899          0.937           0.969     
##   adj. R-squared        0.888           0.892          0.899          0.937           0.969     
##   sigma                 0.289           0.284          0.275          0.216           0.154     
##   F               2700903.714     1406538.330     754405.425     423311.488      521161.443     
##   p                     0.000           0.000          0.000          0.000           0.000     
##   Log-likelihood   -60137.791      -53996.269     -43339.818      37830.414      154124.270     
##   Deviance          28298.689       27291.534      25628.285      15874.910        7992.720     
##   AIC              120281.582      108000.539      86691.636     -75632.827     -308204.540     
##   BIC              120313.783      108043.473      86756.037     -75482.557     -307968.400     
##   N                338946          338946         338946         338946          338946         
## ================================================================================================

Predictions

Example Diamond from BlueNile: Round 1.00 Very Good I VS1 $5,601

#Be sure you’ve loaded the library memisc and have m5 saved as an object in your workspace.

thisDiamond = data.frame(carat = 1.00, cut = "V.Good",
                         color = "I", clarity="VS1")
modelEstimate = predict(m5, newdata = thisDiamond,
                        interval="prediction", level = .95)

exp(modelEstimate)
##        fit     lwr      upr
## 1 5040.436 3730.34 6810.638

Evaluate how well the model predicts the BlueNile diamond’s price. Think about the fitted point estimate as well as the 95% CI.


Final Thoughts

Notes:


Click KnitHTML to see all of your hard work and to have an html page of this lesson, your answers, and your notes!